Consider a random sample X1, X2, ... , Xn from a distribution with pdf f(x; ) = (1 x)1

Chapter 8, Problem 8.6-8

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QUESTION:

Consider a random sample X1, X2, ... , Xn from a distribution with pdf f(x; ) = (1 x)1, 0 < x < 1, where 0 < . Find the form of the uniformly most powerful test of H0: = 1 against H1: > 1.

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QUESTION:

Consider a random sample X1, X2, ... , Xn from a distribution with pdf f(x; ) = (1 x)1, 0 < x < 1, where 0 < . Find the form of the uniformly most powerful test of H0: = 1 against H1: > 1.

ANSWER:

Step 1 of 7

Rewrite the given alternate hypothesis so that the hypothesis is a simple hypothesis on which the Neyman-Pearson lemma can be used.

The hypotheses can be written as,        

Since the hypotheses are now simple, the NP lemma can be used.

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